Symplectic cuts and projection quantization for non-holonomic constraints

Martin Bojowald; Thomas Strobl

doi:10.1142/S0218271803002810

Symplectic cuts and projection quantization for non-holonomic constraints

Martin Bojowald
, Thomas Strobl

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Projection quantization, which is a method to quantize systems with non-holonomic constraints like the condition Det q > 0 in general relativity, is shown to coincide with a reduced phase space quantization in a class of cases which is specified in the main text. This is inferred in the context of geometric quantization using the symplectic cutting technique.

Original language	English (US)
Pages (from-to)	713-725
Number of pages	13
Journal	International Journal of Modern Physics D
Volume	12
Issue number	4
DOIs	https://doi.org/10.1142/S0218271803002810
State	Published - Apr 2003

All Science Journal Classification (ASJC) codes

Mathematical Physics
Astronomy and Astrophysics
Space and Planetary Science

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10.1142/S0218271803002810

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title = "Symplectic cuts and projection quantization for non-holonomic constraints",

abstract = "Projection quantization, which is a method to quantize systems with non-holonomic constraints like the condition Det q > 0 in general relativity, is shown to coincide with a reduced phase space quantization in a class of cases which is specified in the main text. This is inferred in the context of geometric quantization using the symplectic cutting technique.",

author = "Martin Bojowald and Thomas Strobl",

note = "Funding Information: We thank A. Alekseev and H. Kastrup for discussions and J. Klauder for drawing our attention to Ref. 22, in which a related method has been proposed prior to us (cf. also the remark in our conclusions). T. S. is grateful to the Erwin Schr{\"o}dinger Institute in Vienna for hospitality in the period when this work was begun and M. B. to A. Wipf and the TPI in Jena for hospitality during the time when the work was completed.",

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AU - Strobl, Thomas

N1 - Funding Information: We thank A. Alekseev and H. Kastrup for discussions and J. Klauder for drawing our attention to Ref. 22, in which a related method has been proposed prior to us (cf. also the remark in our conclusions). T. S. is grateful to the Erwin Schrödinger Institute in Vienna for hospitality in the period when this work was begun and M. B. to A. Wipf and the TPI in Jena for hospitality during the time when the work was completed.

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N2 - Projection quantization, which is a method to quantize systems with non-holonomic constraints like the condition Det q > 0 in general relativity, is shown to coincide with a reduced phase space quantization in a class of cases which is specified in the main text. This is inferred in the context of geometric quantization using the symplectic cutting technique.

AB - Projection quantization, which is a method to quantize systems with non-holonomic constraints like the condition Det q > 0 in general relativity, is shown to coincide with a reduced phase space quantization in a class of cases which is specified in the main text. This is inferred in the context of geometric quantization using the symplectic cutting technique.

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M3 - Article

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JO - International Journal of Modern Physics D

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ER -

Symplectic cuts and projection quantization for non-holonomic constraints

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